Reddit reviews Superman Adventures Vol. 1

I second the Marvel Adventures line and Superman Adventures.

I'd also recommend:

• The Batman Adventures - It ran from 1992-1995 and was the predecessor to the Gotham Adventures series you mentioned, and the companion title to Superman Adventures.
  
• Bone - A ridiculously fun to read fantasy/adventure story published from 1991 to 2004. Great art, great humor, and it truly appeals to all ages. The colorized version is published in nine digest-sized volumes that are extremely easy to find and very affordable, especially if you buy them used. The original black-and-white version is also available in one volume, but from what I hear there is a lot of gutter loss due to its size and the pages are easy to tear since they are so thin.
  
• Shazam!: The Monster Society of Evil - Good little story from the creator of Bone. I'd especially recommend this for kids who like Superman since it features a similar character. From 2007.
  
• Thor: The Mighty Avenger - Non-canon story about a young Thor. Not only a great kid's comic but one of the best Thor stories ever written. Beautiful artwork, great romance, fun adventures, and lots of appearances from other Marvel characters including Captain America and Iron Man. It ran from 2010-2011 and was sadly cancelled early. Available on Marvel Unlimited.
  
• Ultimate Spider-Man - Not good for smaller children due to lots of dialogue and a moderate amount of violence and sexual content, but excellent for adolescents and teens. I'd recommend it up to issue #128. It's currently being reprinted in this "Ultimate Collection" format which is so far up to volume 6 at issue #71. It ran from 2000-2011 and all of it is available on Marvel Unlimited.
  
  If you're open to older comics (Silver and Bronze Age), then many volumes from the Marvel Epic Collection line are also a good bet, but do a little research since some won't be very kid-friendly. They're fairly affordable reprints of classic stories that aim to reprint the entire history of Marvel's major characters from their inception to usually the mid-nineties (but they're not published in chronological order). They typically retail for around $35 for 400-500 pages of comics.
  
  I'm sure there are more that I'm forgetting, but I hope this helps!

Yup! That's volume 1 of the Millar issues.

They're also doing them in regular-comic-size trades. This is volume 1, with most of the stories scripted by Scott McCloud. Also great stuff: http://www.amazon.com/gp/aw/d/1401258670/ref=mp_s_a_1_sc_1?qid=1458261982&sr=8-1-spell&pi=AC_SX236_SY340_QL65&keywords=suoerman+adventures